§ Motivation for modal logic

possibly A > necessarily (possibly A > B) > necessarily B
 this weakens the precondition
A > (A > B) > B
by needing only possible A
and strengthens the postcondition by spitting out necessarily B
.  Key idea 1: if A is true in no world
w
, then possibly A
that we have is false, and from this we derive explosion.  Key idea 2: if A is true in some world
wa
, then suppose we are in some arbitrary world wr
.  Since
A
is true in wa
, we have possibly A
.  Since
necessarily (possibly A > B)
is true in all worlds, we have (possibly A > B)
.  Since we have both
possibly A
, and possibly A > B
, we derive B
in wr
.  Since
wr
was arbitrary, we then have necessarily B
since B
holds in any arbitrary worlds.
§ Use of this for Kant
 experience of objects is possible.
 it is necessarily the case that if experience is possible, then I must have some way to unite experience.
 thus, necessarily we have unity of experience.
§ Use of this for descartes
 it is possible for me to be certain of something (ie, I think therefore I am)
 it is neecessarily the case that if I can be certain of something, I have clear and distinct perception.
 Therefore, it is necessary that I have clear and distinct perception.